Phase coherent communications provide a higher spectral efficiency (higher data rate for a given bandwidth) than phase incoherent communications and are particularly useful for acoustic communications in a band-limited underwater acoustic channel. The problem is inter-symbol interference (ISI) caused by long multipath delays associated with sound propagation in the underwater channel. As in RF communications, ISI can be removed by channel equalization. Another method is to use time-reversal and/or passive-phase conjugation technique when a vertical array of sources/receivers is available.
One such approach, described in “Adaptive multichannel combining and equalization for underwater acoustic communications,” M. Stojanovic, J. Catipovic and J. G. Proakis, J. Acoust. Soc. Am. 94 (3), 1621-1632 (1993), employs a multi-channel adaptive channel decision feedback equalizer (DFE) in combination with a phase locked loop (PLL). The problem, however, is the reliability of the equalizer in terms of bit error rate (BER) over a large number of packets. Often, in an unsupervised mode, only fractions of the packets are error-free (before error decoding). The reliability gets worse when the source or receiver has motion. One finds that the BER can in many cases be reduced in post-processing by adjusting the parameters in the signal processor. The hope is then to improve the performance by better channel estimation and tracking. As a result, extensive efforts have been devoted to measure the channel impulse responses and relate that to the BER. However, no performance metrics has been found to this date that clearly correlates the performance with the environmental parameters or signal processing parameters. The less than robust performance of the equalizer has thus far prevented unsupervised (or commercial) adaptation of the algorithm in real communication systems.
The performance of coherent acoustic communication systems depends upon channel characteristics that include multipath, spatial and temporal coherence, Doppler effects and ambient noise, effects that exhibit temporal change dependent on local environmental conditions, the amount of movement of the source and receiver platforms and the beam patterns of the sonar transducers. Accordingly, there has been no effective method for predicting the environmental changes and to mitigate against their effects. One finds experimentally while some packets are error free, others in adjacent time periods sometimes have large errors, even when the gross properties of the acoustic channel haven't changed much.
From the signal processing point of view, the unreliability problem is largely attributed to the “catastrophic” error propagation of the DFE when the tap coefficients of the equalizer do not match that of true channel resulting in symbol errors. Impulsive noise can further distort the tap coefficient estimation. The problem is compounded by the fact that the errors are propagated to later symbols, since the incorrect tap coefficients are slowly updated/corrected. This can result in a “catastrophic” condition, namely, incorrect decisions leading to more incorrect decisions. When the accumulated errors exceed a certain threshold (e.g. −8 dB), the processor diverges and cannot recover.
To mitigate the equalizer failure, one approach, described in “Blind adaptive multiple-input decision-feedback equalizer with a self-optimized configuration,” J. Labat and C. Laot, IEEE Trans. Comm. Vol 49, No. 4, 646-654 (2001), is to use blind equalization to recover from the catastrophic condition. Another approach, described in “Channel-estimation-based adaptive equalization of underwater acoustic signals,” M. Stojanovic, L. Freitag and M. Johnson, IEEE OCEANS'99 Vol. 1, 590-595, Seattle Wash. (1999), is to develop improved tracking of the time varying channel impulse response and update the tap coefficients accordingly. A third approach described in “Iterative equalization and decoding techniques for shallow water acoustic channels,” E. M. Sozer, J. G. Proakis, and F. Blackmon, IEEE OCEANS 2001 Vol. 4, 2201-2208 (2001) uses iterative equalization and decoding to correct for symbol errors.
These DFEs' algorithms commonly employ many parameters at the user's discretion. Experimental findings indicate their performance can be sensitive to, and may require some delicate adjustments and balancing of the parameters, which the user cannot foresee. This problem is notably worse when the source or the receiver is moving since another parameter is involved, i.e., the Doppler estimation. Post data analysis demonstrates that many errors are caused by incorrect Doppler estimation in at-sea (real-time) data processing.
For any signal processing method to be useful in practical, un-supervised, applications, it must be robust and reliable under various environmental conditions. In other words, it must adapt to different channel (propagation) conditions as found in various oceans. Robustness can be achieved through the use of some invariant features of the signal and/or well-founded (signal processing) principles. Two performance measures for robustness and reliability are: the BER for a given input signal-to-noise ratio and the percentage of the packets that achieve the given BER. Another issue that involves signal processing has to do with practical (system) constraints, namely, (computation) power limitation for a practical acoustic modem. To assure fast convergence, the DFE normally uses a recursive least square (RLS) algorithm. This algorithm is computationally intensive. The number of calculations is proportional to (NM)2, where N is the number of receiver channels and M is the total number of feed forward and feedback coefficients per channel. Conventional channel equalizer requires feedback taps that cover the entire multipath spread; the number can easily exceed 100 per channel. A sparse DFE determines the positions of significant taps by estimating the channel impulse response whose magnitude exceeds a pre-determined threshold. A significantly smaller number of tap coefficients are used resulting in a substantial saving in numerical computations. However, one finds that in practice the number of taps (from the above estimate) needs to be enlarged by a certain percentage (e.g. 10%) to allow for fluctuations in the multipath arrival time (over the packet duration) due to temporal variations of the propagation medium, and signal dilation/compression by time varying Doppler shift. Poor performance can result if no provision is given for the “rotation and drift” of the tap coefficients. The sparse channel estimation was found as one of the major metrics in performance analysis of experimental data. The reasons can be traced to: (1) inaccurate estimation of weak arrivals due to insufficient input signal-to-noise ratio, and (2) temporal variation of multipath arrivals within a packet due to source changing range and depth. Note that the number of feed forward and feedback coefficients must be determined in situ.
Another approach described in “Reduced-complexity spatial and temporal processing of underwater acoustic communication signals,” M. Stojanovic, J. Catipovic and J. G. Proakis, J. Acoust. Soc. Am. 98 (2), 961-972 (1995), obtains reduction in computational complexity by transforming the receiver data from the element space to the beam space, and applying multi-beam DFE. This reduced complexity multi-channel combining method is effective when a large number of receivers are used since the numbers of beams that contain the signal energy are usually small (arrival angle normally limited to <15° from the horizon). This approach is not useful when only a small number of receivers are available as often is the case in practice. Not only does the computational advantage disappear but also the beam widths are too wide to track the signal arrival angles. Also, beam diversity has not been shown to be as effective as element (spatial) diversity.
Another approach for underwater acoustic communication using the so-called passive-phase conjugation method is based on the concept of (passive) time-reversal. An active time reversal method uses the time-reversed channel impulse response function to modulate the transmitted signal. The method is illustrated in “An initial demonstration of underwater acoustic communication using time reversal,” J. Edelmann et al, IEEE J. Oceanic Eng. 27, 602-609 (2002). The time-reversed impulse response after (back) propagation through the ocean waveguide is converted back to the original pulse plus some side lobes. Given a vertical array of sources, the back-propagated signal is focused at the location of the original probe source. Active time reversal requires two-way transmissions. Passive-phase conjugation carries out this “back-propagation” process in the computer using only one-way transmission as illustrated in “Underwater acoustic communication by passive-phase conjugation: Theory and experimental results,” D. Rouseff et al, IEEE J. Oceanic Eng. 26, 821-831 (2001). A probe signal is sent first, from which the channel impulse response function is estimated. The received data is convolved with the phase conjugated or time-reversed channel impulse response and summed over all the receiver channels. The summed data should have minimal ISI if a vertical array of receivers is used. Time-reversal or passive-phase conjugation minimizes ISI but does not totally remove it. The advantage is that the receiver processor is simple. Time-reversal or passive-phase conjugation assumes that the underwater acoustic communication channel is time invariant. For a time varying ocean, the channel impulse response needs to be re-estimated by channel tracking.